This invention is related to the determination of log quality using redundant measurements.
This invention is directed toward quality control in the measurement of geophysical parameters of earth formations penetrated by a borehole. Co-pending U.S. patent application Ser. No. 08/675,178, filed on Jul. 3, 1996 discloses a method for quality control of propagation resistivity techniques using spaced transmitters operating at different frequencies and a plurality of longitudinally spaced receivers. An electromagnetic wave is propagated from the transmitting antenna coil into the formation in the vicinity of the borehole and is detected as it pass the receiving antennas. The basic or xe2x80x9crawxe2x80x9d parameters measured by the receivers are the phase and the amplitude of the passing wave. The downhole instrument is conveyed along the borehole making a plurality of raw measurements as a function of depth within the borehole from which geophysical parameters of interest are computed as a function of depth within the borehole. It is quite common in the prior art to first combine raw data measurement and then to compute parameters of interest from these process measurements. A typical example is the computation of apparent resistivity from the difference in phase of signals detected at receivers at different longitudinal spacings from the transmitter. A second example is the computation of apparent resistivity from the ratio of the amplitude of signals detected at the longitudinally space receivers. Such preprocessing or data combination is performed primarily to eliminate the gross effects of the borehole and is well known in the prior art.
The ""178 application is directed toward the simultaneous measurement of a plurality of parameters associated with the formation and borehole environment, and a quantitative measure of the quality of such raw measurements or uncertainty associated with such raw measurements. Parameters of interest selected may include the resistivity of the formation from which hydrocarbon saturation is computed, invasion profiles of the drilling fluid which are indicative of the permeability of the formation, and perhaps physical characteristic of the well bore itself such as diameter, ellipticity, and rugosity.
In the ""178 application, non-linear inversion techniques are used to determine the set of selected unknown parameters which, through the model, predicts a tool response which most closely matches the thirty two measured raw data points. The predicted tool responses and the measured tool responses will exhibit no discrepancies only if (a) there is no error associated with the measured data and (b) if the model represents without error the response of the instrument in every encountered borehole and formation condition. This is because there are more measured data points than unknown variable parameters in the model. Any degree of non-conformance or xe2x80x9cmismatchxe2x80x9d of the model data and the measured data is a measure of inaccuracy of either the data or the model or both the data and the model. In all cases the determined non-conformance is treated as a quality indicator for the determined parameters of interest. In other words, an uncertainty is attached to each parameter selected by the analyst based upon the goodness of fit between the model and the measured data. Obtaining formation parameters from observations at multiple frequencies and/or multiple source-receiver offsets involves the solution of an overdetermined system of equations.
A similar situation arises in obtaining formation parameters in induction logging techniques. For example, U.S. Pat. No. 5,452,761 to Beard et al, having the same assignee as the present application and the contents of which are fully incorporated herein by reference, discloses an apparatus and method for digitally processing signals received by an induction logging tool having a transmitter and a plurality of receivers. An oscillating signal is provided to the transmitter, which causes eddy currents to flow in a surrounding formation. The magnitudes of the eddy currents are proportional to the conductivity of the formation. The eddy currents in turn induce voltages in the receivers. The received voltages are digitized at a sampling rate well above the maximum frequency of interest. The digitizing window is synchronized to a cycle of the oscillating current signal. Corresponding samples obtained in each cycle are cumulatively summed over a large number of such cycles. The summed samples form a stacked signal. Stacked signals generated for corresponding receiver coils are transmitted to a computer for spectral analysis. Transmitting the stacked signals and not all the individually sampled signals, reduces the amount of data that needs to be stored or transmitted. A Fourier analysis is performed on the stacked signals to derive the amplitudes of in-phase and quadrature components of the receiver voltages at the frequencies of interest. From the component amplitudes, the conductivity of the formation can be accurately derived. The Beard patent also teaches the use of analyzing data at multiple frequencies. These multiple frequencies may be obtained either by activating the transmitter at a plurality of frequencies, or, in a preferred embodiment, by a harmonic analysis of the data. As taught in the Beard patent, single frequency data modulated by a square pulse provides a signal that is rich in odd harmonics. Observations at multiple frequencies and solving for formation parameters gives an overdetermined system of equations, as in the ""178 application.
U.S. Pat. No. 5,666,057 to Beard et al, the contents of which are fully incorporated herein by reference, teaches a multifrequency method of correcting for the so-called xe2x80x9cskin-effectxe2x80x9d and obtaining apparent conductivity of formations using induction logging tools. U.S. Pat. No. 5,889,729 to Frenkel et al having the same assignee as the present application, and the contents of which are fully incorporated herein by reference, discloses a method for 2-D inversion of induction logging data. Included therein is a step of 2-D forward modeling of induction logging data and the inversion of such data. U.S. Pat. No. 5,781,436 to Forgang et al, and U.S. Pat. No. 5,999,883 to Gupta et al., the contents of both of which are incorporated herein by reference, disclose the inversion of transverse induction logging data. A Transverse Induction Logging Tool (TILT) from which such data are obtained comprises a plurality of transmitters and receivers that have axes inclined to each other. Where the borehole axis is inclined to the bedding, such devices are able to determine apparent vertical and horizontal conductivities that are able to delineate resistive hydrocarbon bearing beds more accurately than conventional induction logging tools.
Solution of overdetermined systems of equations is also involved in Nuclear Magnetic Resonance (NMR) logging. This technique involves using NMR logging tools and methods for determining, among other things porosity, hydrocarbon saturation and permeability of the rock formations. The NMR logging tools are utilized to excite the nuclei of the fluids in the geological formations in the vicinity of the wellbore so that certain parameters such as spin density, longitudinal relaxation time (generally referred to in the art as xe2x80x9cT1xe2x80x9d), and transverse relaxation time (generally referred to as xe2x80x9cT2xe2x80x9d) of the geological formations can be estimated. From such measurements, porosity, permeability, and hydrocarbon saturation are determined, which provides valuable information about the make-up of the geological formations and the amount of extractable hydrocarbons.
U.S. Pat. No. 5,023,551 issued to Kleinberg discloses an NMR pulse sequence that has an NMR pulse sequence for use in the borehole environment which combines a modified inversion recovery (FIR) pulse sequence with a series of more than two, and typically hundreds, of CPMG pulses according to
[Wi-180-TWi-90-(t-180-t-echo)j]i 
where j-1,2, . . . J and J is the number of echoes collected in a single Carr-Purcell-Meiboom-Gill (CPMG) sequence, where i=1, . . . I and I is the number of waiting times used in the pulse sequence, where Wi are the recovery times, TWi are the wait times before a CPMG sequence, and where t is the spacing between the alternating 180xc2x0 pulses and the echo signals. Although a conceptually valid approach for obtaining T1 information, this method is extremely difficult to implement in wireline, MWD, LWD or MWT applications because of the long wait time that is required to acquire data with the different TWs.
Data may be acquired with different wait times and/or at different frequencies. In such cases, redundant measurements are made of basically the same physical parameters, viz., the distribution of T1 and T2 values of the formation. The data may be acquired in the same or different logging passes and it would be desirable to have a method for checking the consistency of the data, the validity of the model, and the reliability of the measurements.
The current invention provides means and methods for determining error which can be related to uncertainty associated with geophysical parameters measured with a downhole instrument of any of the types previously described. The user of the information, or xe2x80x9canalystxe2x80x9d, selects the parameters of interest which might include the resistivity (or conductivity) of the formation, the dielectric constant of the formation, the longitudinal and transverse relaxation times, or perhaps the degree to which drilling fluids invade the formation in the vicinity of the borehole. The analyst""s primary interests are usually the determination of the hydrocarbon saturation, porosity and permeability of the formations penetrated by the borehole. It is highly desirable to make such measurements while drilling or soon after the drilling of the well borehole so that critical economic concerning the amount and producibility of hydrocarbons in place can be made. Based upon this information, the well will either be completed or abandoned. The accuracy and precision of geophysical parameters selected to make such critical decisions is also of prime importance. The error measurements provided by the current invention can also be used to indicate equipment malfunctions of both the electrical and mechanical types. Although prior art teaches means and methods of measuring a wide range of geophysical parameters using electromagnetic techniques, little, if any, emphasis is placed upon determining the quality of the measurements. Usually the analyst can only rely on past experience in assigning, at best, qualitative estimates of the quality of the measurements obtained from the borehole instrument and associated system. Any error analysis is usually performed long after the measurements are made and usually not at the well site. Stated another way, prior art does not provide means and methods for determining the quality of electromagnetic based geophysical measurements in real-time, although real-time or near real-time economic and operational decisions are made based upon these measurements.
There is critical need for quantitative indications of the quality of geophysical measurements made in formations penetrated measurements simultaneous with the measurements made in formations penetrated by a borehole. More particularly there is a need for such quality measurements simultaneous with the measurements of parameters of interest. Knowledge of these parameters weighs so heavily in decision to complete or abandon the well. The present invention provides this very information by providing means and methods for measuring geophysical parameters selected by the analyst and simultaneously yielding quantitative measurements of the quality or error associated with the measurements of the selected parameters.
This invention is directed toward the redundant measurement of a plurality of parameters associated with the formation and borehole environment, and a quantitative measure of the quality of such raw measurements or uncertainty associated with such raw measurements. The measurements may be made simultaneously or in multiple passes. In the case of resistivity logging, parameters of interest selected may include the resistivity of the formation from which hydrocarbon saturation is computed, invasion profiles of the drilling fluid which are indicative of the permeability of the formation, and perhaps physical characteristic of the well bore itself such as diameter, ellipticity, and rugosity. The borehole related parameters might be used by the analyst to determine, as an example, the rock mechanics of the formation. In the case of NMR logging, one of the parameters of interest is the T1 distribution time that characterizes the porosity of the formatin. As discussed previously, errors associated with the measurements are critical in the decision concerning-completion or abandonment of the well. Information concerning completion or abandonment of the well. Information concerning rock mechanics might guide the analyst in perforating after casing has been set or even in the design of hydraulic formation fracture operations subsequent to the setting of casing. The invention allows the analyst to choose parameters needed to make informed decisions as long as the total number of chosen parameters is less than the number of measurements made. Choices of parameters can vary from well to well depending upon need.
In one embodiment of the invention, measurements are made with an induction logging tool having a plurality of transmitters and receivers. In conventional logging tools, the transmitters and receiver coils are coaxial with the tool axis. In Transverse Induction Logging Tools (TILT), one or more of the transmitter and receiver coils are inclined to the axis of the tool so as to give measurements indicative of the horizontal and vertical conductivity of the formation. Two types of problems are addressed: one is the so-called xe2x80x9cskin-effectxe2x80x9d correction and the other is the inversion of the corrected data to give a layered model of resistivity of the formation. Both types of problems involve solution of an overdetermined set of equations.
In another embodiment, the method of the invention is used in the analysis of NMR data. Two possible applications are addressed. In one application, data acquired with multiple wait times are analyzed and compared for quality control. In another application, multifrequency NMR data are analyzed for consistency.